C
C-------------------------------------------------------------------------C !MT000324-1
C SUBRUTINA PIANOR C !MT000324-1
C-------------------------------------------------------------------------C !MT000324-1
C
SUBROUTINE PIANOR(XP,YP,X1,Y1,X2,Y2,HH,GG,MU1,MU2,
@ QQQ,QQP,DD1,DD2,SS1,SS2)
C
C La subrutina PIANOR calcula las constantes de integración
C analíticamente según la nueva formulación en variable compleja
C para la evaluación de las tensiones en puntos internos
C
IMPLICIT NONE
C
INCLUDE '_param.for'
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C VARIABLES EXTERNAS (ENTRADA)
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C
C REAL*8 BMAS,GAMMA,B11,B22
REAL*8 XP,YP,X1,Y1,X2,Y2
COMPLEX*16 MU1,MU2
COMPLEX*16 QQQ(3,2,2),QQP(3,2,2)
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C VARIABLES EXTERNAS (SALIDA)
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C
REAL*8 HH(3,4),GG(3,4)
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C VARIABLES INTERNAS
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C
REAL*8 ARG(2,2),THETA(2),FF(2,2),DF(2)
C REAL*8 HHAUX(3,2),XNUE,YNUE
REAL*8 XB,XA,YB,YA,ELON
REAL*8 CMOD,DIS
COMPLEX*16 IC,Z(2,2),ZZ,TK(2),LNC
COMPLEX*16 DD1(3,2),DD2(3,2),SS1(3,2),SS2(3,2)
C
INTEGER L,K,M,N,J
C
C CMOD(Z) calcula el modulo del numero complejo Z
CMOD(ZZ)=DSQRT(DREAL(ZZ)*DREAL(ZZ)+DIMAG(ZZ)*DIMAG(ZZ))
C DIS(XA,YA,XB,YB) calcula la distancia entre dos puntos A y B
DIS(XA,YA,XB,YB)=DSQRT((XB-XA)*(XB-XA)+(YB-YA)*(YB-YA))
C LNC(L,K) calcula el logaritmo natural de Z(L,K)
LNC(L,K)=(DLOG(CMOD(Z(L,K)))+IC*ARG(L,K))
C
IC=(0.D00,1.D00)
FF(1,1)=1.D00
FF(1,2)=0.D00
FF(2,1)=0.D00
FF(2,2)=1.D00
ELON=DIS(X1,Y1,X2,Y2)
DO M=1,2
DF(M)=(FF(M,2)-FF(M,1))/ELON
END DO
Z(1,1)=(X1-XP)+MU1*(Y1-YP)
Z(1,2)=(X2-XP)+MU1*(Y2-YP)
TK(1)=((X2-X1)+MU1*(Y2-Y1))/ELON
if(.NOT.(MU1.EQ.MU2)) THEN
Z(2,1)=(X1-XP)+MU2*(Y1-YP)
Z(2,2)=(X2-XP)+MU2*(Y2-YP)
TK(2)=((X2-X1)+MU2*(Y2-Y1))/ELON
END IF
C
C Si las raices del polinomio caracteristico son diferentes
C
if(.NOT.(MU1.EQ.MU2)) THEN
CALL ARGU4(Z,ARG,2)
DO L=1,2
THETA(L)=DSIGN(1.D00,DREAL(Z(L,1))*DIMAG(Z(L,2))-DIMAG(Z(L,1))
@ *DREAL(Z(L,2)))*DATAN2(DABS(DREAL(Z(L,2))*
@ DIMAG(Z(L,1))-DREAL(Z(L,1))*DIMAG(Z(L,2))),
@ DREAL(Z(L,1))*DREAL(Z(L,2))+DIMAG(Z(L,1))*DIMAG(Z(L,2)))
END DO
DO J=1,3
C
C J es el indice de las tensiones
C J=1 ----- SIGMA11
C J=2 ----- SIGMA12
C J=3 ----- SIGMA22
DO N=1,2
C N es el indice de la coordenada segun el eje 1 o 2
DO M=1,2
C M es el indice del nodo
C M=1 ----- NODO K
C M=2 ----- NODO K+1
HH(J,2*(N-1)+M)=0.d00
GG(J,2*(N-1)+M)=0.d00
C
DO L=1,2
C
HH(J,2*(N-1)+M)=HH(J,2*(N-1)+M)-DREAL(QQP(J,N,L)*(FF(M,2)
@ -FF(M,1)+((FF(M,1)*Z(L,2)-FF(M,2)*Z(L,1))*
@ (DLOG(CMOD(Z(L,2))/CMOD(Z(L,1)))+IC*THETA(L))
@ /(Z(L,2)-Z(L,1))))/TK(L))
GG(J,2*(N-1)+M)=GG(J,2*(N-1)+M)+DREAL(QQQ(J,N,L)*((FF(M,2)/
@ Z(L,2))-(FF(M,1)/Z(L,1))-((FF(M,2)-FF(M,1))*
@ (DLOG(CMOD(Z(L,2))/CMOD(Z(L,1)))+IC*THETA(L))
@ /(Z(L,2)-Z(L,1)))))
END DO
END DO
END DO
END DO
ELSE
C
C Si las raices del polinomio caracteristico son iguales
C
CALL ARGU4(Z,ARG,1)
DO J=1,3
DO N=1,2
DO M=1,2
HH(J,2*(N-1)+M)=0.D00
GG(J,2*(N-1)+M)=0.D00
DO K=1,2
HH(J,2*(N-1)+M)=HH(J,2*(N-1)+M)+DREAL(((-1.D00)**(K))*
@ (DD1(J,N)*((FF(M,K)*LNC(1,K)/
@ TK(1))-(DF(M)*Z(1,K)*(LNC(1,K)-1.D00)/
@ (TK(1)*TK(1))))+DD2(J,N)*((FF(M,K)*
@ ((CONJG(TK(1))*LNC(1,K)/TK(1))-
@ (CONJG(Z(1,K))/Z(1,K)))/TK(1))-
@ (DF(M)*((2.d00*CONJG(TK(1))*Z(1,K)-
@ TK(1)*CONJG(Z(1,K)))*LNC(1,K)-
@ 2.D00*CONJG(TK(1))*Z(1,K))/
@ (TK(1)*TK(1)*TK(1))))))
C
GG(J,2*(N-1)+M)=GG(J,2*(N-1)+M)+DREAL(((-1.D00)**(K))*
@ (SS1(J,N)*(FF(M,K)/Z(1,K)-DF(M)*
@ LNC(1,K)/TK(1))+
@ SS2(J,N)*(FF(M,K)*CONJG(Z(1,K))/Z(1,K)-
@ DF(M)*(CONJG(TK(1))*LNC(1,K)/TK(1)-
@ CONJG(Z(1,K))/Z(1,K))/TK(1))))
END DO
END DO
END DO
END DO
END IF
C
C Giro de HH
C
c DO J=1,3
c DO N=1,2
c HHAUX(J,N)=HH(J,N)
c END DO
c END DO
c XNUE=(Y2-Y1)/DSQRT((X2-X1)**2.D00+(Y2-Y1)**2.D00)
c YNUE=-(X2-X1)/DSQRT((X2-X1)**2.D00+(Y2-Y1)**2.D00)
c DO J=1,3
c DO N=1,2
c HH(J,N)=HH(J,N)*XNUE+HH(J,N+2)*YNUE
c HH(J,N+2)=-HHAUX(J,N)*YNUE+HH(J,N+2)*XNUE
c END DO
c END DO
RETURN
END
e-REdING. Biblioteca de la Escuela Superior de Ingenieros de Sevilla.
